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研究生: 尹菀珊
Yin, Wan-Shan
論文名稱: 運用螺旋理論於人體足部力量分析
Foot Reaction Analysis of Whole Body Dynamic via Screw Theory
指導教授: 蔡明俊
Tsai, Ming-June
學位類別: 碩士
Master
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2015
畢業學年度: 103
語文別: 英文
論文頁數: 75
中文關鍵詞: 全身動力學螺旋理論ZMP足部力量
外文關鍵詞: Whole body dynamic analysis, Screw theory, Zero moment point, Foot reaction
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  • 本研究提出使用三維人體模型來計算全身運動參數,且運用螺旋理論提出一新方法求取人體的零力矩點(ZMP)。根據專業武術家表演連續25秒的武術動作執行本研究所提出的方法,然後比較以螺旋理論求得的ZMP與使用常規的Vukobratovic法所求得的ZMP的差異。最後,運用螺旋理論中的二系統幾何特性來推導雙腳觸地時的數學模型,該系統可用12條限制式及2個自由參數描述,然後以最小內力矩為目標函數求最佳解。結果顯示,自由參數越多所求得的內力矩越小,且人體所受的內力與內力矩可由作用於雙腳的螺旋求得。

    This study proposes a method for determining the dynamic parameters of human motion using a three-dimensional (3D) whole human body model. Accordingly, the wrench screw exerts on the body ($0) is found via Newton/Euler equations. Furthermore, the zero moment point (ZMP) of the $0 is found from the definition of the screw. The comparison of the proposed method and the conventional Vukobratovic method is demonstrated by evaluating the whole body dynamics over the course of a 25-second sequence of continuous moves performed by a professional martial arts practitioner. Using linear dependency of the reaction screws of both feet and $0, there are 12 equations to solve 14 unknowns. Two parameters are characterized by the geometry of the two-system, namely a cylindroid. Therefore, optimal foot reactions can be computed by the assumption of minimum internal moment generated by the foot contact points. It is shown that the two-system is given more degrees of freedom, the internal moment can reach a smaller value. Moreover, the internal forces and internal moments acting on the body are determined by the reaction screws of both feet.

    中文摘要 I Foot Reaction Analysis of Whole Body Dynamic via Screw Theory II ACKNOWLEDGEMENTS VII TABLE OF CONTENTS VIII LIST OF TABLES XI LIST OF FIGURES XII Chapter 1. Introduction 1 1.1 Motivation and Purpose 1 1.2 Literature Review 2 1.3 Outline 3 Chapter 2. Structure of the Human Model 4 2.1 Structure of the Human Link 4 2.2 Introduction of Multi-coordinate Systems 7 2.3 Geometric Parameters of Links 8 Chapter 3. Three-Phases Inverse Kinematics 16 3.1 Forward Kinematics 16 3.2 The 1st Phase Inverse Kinematics 18 3.2.1 One Degree of Freedom 19 3.2.2 Two Degrees of Freedom 19 3.2.3 Three Degrees of Freedom 21 3.2.4 Four Degrees of Freedom 22 3.3 The 2nd Phase Inverse Kinematics 23 3.4 The 3rd Phase Inverse Kinematics 25 3.5 Error Analysis 26 Chapter 4. Calculation of Whole Body Dynamics 37 4.1 Geometric Parameters of Whole body 37 4.1.1 Mass and centroid 37 4.1.2 Principal Axes of Inertia 38 4.2 Dynamic Parameters of Whole Body 39 4.2.1 Kinematic Parameters of Whole Body 39 4.2.2 Force and Moment of Whole Body 42 4.2.3 Implement Results 43 4.3 Zero Moment Point 48 4.3.1 Vukobratovic Method 48 4.3.2 Screw Method 50 4.3.3 Results 52 Chapter 5. Foot Reaction Analysis 53 5.1 Foot Status 53 5.2 Support Polygon and Foot Centroid 54 5.3 Foot Reaction Analysis Using Screw Theory 56 5.3.1 Single Support 56 5.3.2 Double Support 57 Chapter 6. Optimizations of Double Support Phase 62 6.1 Construct a New Coordinate System 62 6.2 Static Situation 64 6.3 Dynamic Situation 68 Chapter 7. Discussion and Recommendation 74 7.1 Contribution 74 7.2 Discussion 74 7.3 Future Work 75 References 76

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